A bandgap reference circuit using bipolar transistors is widely known as conventional art. The basic configuration of the circuit and its operational principle is published in, for example, Japanese Laid-open Patent Application No. 11-121694 and a book “Analysis and Design of Analog Integrated Circuits”, P. R. Gray, et al., 1977, John Wiley & Sons.
The principle will be described below.
FIG. 8 is a circuit diagram showing a conventional circuit for generating a reference voltage.
The bandgap reference circuit includes the following: an operational amp 1; a third resistance R6 and a bipolar transistor Q3 connected in series between the output terminal of the operational amp 1 and the ground; a second resistance R5, a first resistance R4, and a bipolar transistor Q4 connected in series between the output terminal of the operational amp 1 and the ground. The collector and the base of each bipolar transistor Q3 and Q4 are electrically connected to each other. The bipolar transistors Q3 and Q4 are connected as diodes.
The non-inverted input terminal (+) of the operational amp 1 is connected to a connection point 13 between the third resistance R6 and the transistor Q3. The inverted input terminal (−) of the operational amp 1 is connected to a connection point 15 between the first resistance R4 and the second resistance R5.
The output of the operational amp 1 is fed back into the input terminals using the first resistance R4, the second resistance R5, and the third resistance R6, and is output as the output of the bandgap reference circuit. The output of the operational amp 1 is used as the reference voltage Vref.
The size of the transistor Q3 is different from that of the transistor Q4. The ratio of current flowing through the transistors Q3 and Q4 needs to be precisely adjusted. Accordingly, the transistor Q4 is often constructed by a plurality of transistors connected in parallel, having the same layout pattern as the transistor Q3.
The imaginary short of the operational amp 1 givesVbe3=Vbe4+Vr4  (1)where Vbe3 is the forward voltage of the pn junction between the base and the emitter of the transistor Q3, Vbe4 is the forward voltage of the pn junction between the base and the emitter of the transistor Q4, and Vr4 is a voltage applied to the first resistance R4.
Vr4 is equal to the difference between Vbe3 and Vbe4, thusΔVbe=Vbe3−Vbe4  (2)
For each transistor Q3 and Q4,Vbe3=Vt*ln(I3/Is3) and  (3)Vbe4=Vt*ln(I4/Is4)  (4)where Vt is the thermal voltage Vt=kT/q (k: Boltzmann constant, T: absolute temperature, and q: elementary electric charge). I3 is the current flowing through the third resistance R6 and the transistor Q3, and I4 is the current flowing through the second resistance R5, the first resistance R4, and the transistor Q4. Is3 and Is4 are the saturation currents of the transistors Q3 and Q4, respectively. For R5 and R6, the imaginary short of the operational amp 1 givesI4*R5=I3*R6  (5)Thus,I4=I3*R6/R5  (6)
Substitution of (2), (3), and (4) givesΔVbe=Vt*ln((I3*Is4)/(I4*Is3))  (7)
Combining (6) and (7),ΔVbe=Vt*ln((R5*Is4)/(R6*Is3))  (8)
The voltage of R5 isΔVbe*R5/R4  (9)
Because of the imaginary short of the operational amp 1, (9) plus Vbe3 is equal to Vref,Vref=ΔVbe*R5/R4+Vbe3  (10)
Substitution of (10) and (8) givesVref=(R5/R4)*Vt*ln((R5*Is4)/(R6*Is3))+Vbe3  (11)
In the case where the array of a plurality of bipolar transistors of exactly the same layout pattern as the transistor Q3 are used as the transistor Q4, the saturation current of Q4 isIs4=n*Is3  (12)
Combining (11) and (12) givesVref=(R5/R4)*Vt*ln(n*R5/R6)+Vbe3  (13)
The resistances R1, R2, and R3 and the number “n” of bipolar transistors are constants determinable by design. Setting KK=(R5/R4)ln(n*R5/R6)  (14)
(13) becomesVref=K*Vt+Vbe3  (15)
As showed in (3), Vbe3 depends on both Vt and Is3. Since Vt=kT/q, Vt is a linear function of a temperature T of which inclination is k/q, 0.086 mV/° C. The saturation current Is3 of the bipolar transistor Q3 also depends on the temperature. The saturation current of a bipolar transistor generally depends on a temperature substantially linearly and its inclination is about −2 mV/° C. Accordingly, if K is set equal to about 23 (≅−Is/Vt), it is possible to substantially cancel the temperature dependency of Vref.
In practice, however, the temperature dependency of Vref disperses due to the dispersion in the forward-direction voltages Vbe of the bipolar transistors and in the resistances of the resistors, and due to the offset voltage of the operational amp.
Japanese Patent Laid-open Application No. 11-121694 discloses a technique to control the temperature dependency of a bandgap reference circuit by adjusting the resistance provided therein using a fuse.
However, there is a factor that degrades the temperature dependency inherent in the bandgap reference circuit. The factor is the temperature dependency of the resistances causing ΔVbe.
The temperature dependency of resistance of resistors provided in a large scale integrated circuit (LSI) in which a bandgap reference circuit is used is, in the case of a diffusion resistance using a diffusion layer, about 1000-1500 ppm/° C., and in the case of a poly silicon resistance of which sheet resistance is several dozens ohm, several hundreds ppm/° C. Accordingly, as for the resistance of the resistor generating ΔVbe, as the temperature rises, the load current flowing through the resistor is reduced. Even if the load current is reduced, the resistance ratio is not affected. However, the linear temperature dependency of Vbe is affected since the temperature dependency of the forward-direction voltage Vbe of the bipolar transistor depends on the load current.
FIG. 9 is a graph showing the actual data of temperature dependency of forward-direction voltage Vbe of a bipolar transistor. The y-axis indicates a forward-direction voltage Vbe (mV), and the x-axis indicates a temperature (° C.). The data are measured for the load current of 10 nA, 100 nA, and 1 μA. The data show that the negative inclination is gradually increased as the load current is increased in the order of 10 nA, 100 nA, and 1 μA.
FIG. 10 is a graph showing actual data of temperature dependency of Vt of a bipolar transistor. The y-axis indicates Vt (mV), and the x-axis indicates a temperature (° C.). The measurement was taken for the load currents of 10 nA, 100 nA, and 1 μA. Vt shows a temperature dependency as obtained in theory and does not depend on the load current as the load current dependency is cancelled when Vt is calculated by subtracting the forward direction voltages Vbe.
If the load currents I3 and I4 do not depend on temperature, the forward direction voltages Vbe3 and Vbe4 linearly depend on the temperature. As showed in FIG. 9, however, the load currents I3 and I4 depend on the temperature due to the temperature dependency of the resistances R4, R5, and R6. Accordingly, the linearity in the temperature dependency of the forward direction voltage Vbe3 and Vbe4 is disturbed.
To the contrary, as showed in FIG. 10, the temperature dependency of Vt does not depend on the load current. Accordingly, as expressed by (15),Vref=K*Vt+Vbe3becomes dependent on the temperature.